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Notes on an approximate Method of Valuation of Whole-Life Assurances, with Allowance for Selection

Published online by Cambridge University Press:  18 August 2016

Thomas G. Ackland
Thomas G. Ackland
Affiliation:
Institute of Actuaries;
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Extract

The object of the following notes is to state somewhat more fully and formally a method (first published in the Insurance Record for 10 March 1905) of approximating to the reserves required for whole-life assurances, with due regard to the influence of selection; and to illustrate the practical application of the method.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 40 , Issue 1 , January 1906 , pp. 42 - 98
Copyright
Copyright © Institute and Faculty of Actuaries 1906

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References

page 48 note * It would probably have been more satisfactory to apply Prof. Karl Pearson's method of moments more directly, by deducing the values of the functions At, Bt and Ct from three equations, based on thefirst, second and third “moments” of the function π[x]+t for successive values of x, at a given value of t; in which case the sums of the true and approximate values of the function would have been identical, as well as their second and third summations. It was, however, found that the arithmetical labour involved, where 41 consecutive values of the function were employed, was very considerable; and the above method, whilst much less laborious, was thought to be quite sufficiently accurate for the practical purposes required, although not so defensible on theoretical grounds.

page 50 note * Relative amounts assured were employed, rather than actual amounts, as the latter made the resulting figures of the Model Office unmanageably large.

page 59 note * In order to illustrate a fundamental principle, referred to by Mr. Lidstone, and other speakers, in the course of the discussion on the Paper, the several functions given in Table IX, have been arranged in the order of the average ratios in column (4), and the average ages in column (5).

page 80 note * The general formula, deduced as above, was arrived at after I had seen Mr, Lidstone's more elegant demonstration of the same result.